HSC Mathematics Extension 1: complete 2026 guide (modules, exam, scaling, strategy)

HSC Mathematics Extension 1 is the 1-unit course that sits on top of Mathematics Advanced. Together they form a 3-unit study and the two papers are sat as separate HSC exams. Extension 1 is taken by students aiming at high ATARs, STEM degrees, or commerce and actuarial pathways.

This page is the index. Below you will find the topic breakdown, exam structure, scaling notes, study strategy, and links to every dot point and deep guide we have.

Two syllabuses are live in 2026

HSC Mathematics Extension 1 is in a syllabus transition.

If you are sitting the HSC in 2026 (currently Year 12), you follow the 2017 syllabus. Topics: Functions, Trigonometric Functions, Calculus, Combinatorics (Year 11 ME-A1), Proof by Induction, Vectors (Year 12 ME-V1), and the Binomial Distribution.

If you are starting Year 12 in Term 4 2026 (the 2027 HSC), you follow the new Mathematics Extension 1 11-12 Syllabus (2024). Most of the mathematics carries over, but all calculus is now Year 12, vectors now include three dimensions and motion in vector form, the sampling distribution of the mean and the central limit theorem replace sample proportions, area between curves and 3D trigonometry move in from Advanced, and the t-formulae, products to sums and the pigeonhole principle leave the course. Read what's changed in the new syllabus.

The module codes and dot-point pages on this hub follow the 2017 syllabus; where the mathematics is unchanged they apply to both.

The seven topics

Functions (ME-F1, ME-F2)

Polynomial functions, division algorithm, remainder and factor theorems, multiple roots and multiplicity, polynomial inequalities, parametric equations, and graphs of reciprocal and rational functions.

Trigonometric functions (ME-T1, ME-T2, ME-T3)

Inverse trigonometric functions ($\arcsin$, $\arccos$, $\arctan$) including their graphs, domains and ranges. Sum, difference, double and product-to-sum identities. The auxiliary angle technique. General solutions of trigonometric equations and the t-formula (Weierstrass substitution).

Calculus (ME-C1, ME-C2, ME-C3)

Related rates and exponential growth and decay. Integration by substitution, including reverse chain rule cases. Integration giving inverse trigonometric functions. Volumes of revolution. Separable differential equations and their applications. Projectile motion.

Combinatorics and the binomial theorem (ME-A1)

Permutations, combinations, the pigeonhole principle, and the binomial theorem with Pascal's triangle.

Proof by mathematical induction (ME-P1)

Induction on series, divisibility statements, and inequalities. Structuring an induction proof: base case, induction hypothesis, induction step, conclusion.

Vectors (ME-V1)

Two-dimensional vectors, vector arithmetic, magnitude and direction. The scalar (dot) product, the angle between two vectors, and orthogonality. Projection of one vector onto another. Parametric vector equations of lines. Geometric proofs using vectors.

Statistical analysis (ME-S1)

The Bernoulli trial, the binomial distribution, mean and variance of $X \sim B(n, p)$, exact binomial probabilities, and the normal approximation of the binomial.

Exam structure

HSC Mathematics Extension 1 is sat as a single paper of 2 hours working time plus 10 minutes reading time, in addition to either the Mathematics Advanced paper or, for Extension 2 students, the Mathematics Extension 2 paper.

• Section I: Multiple choice, 10 questions, 10 marks
• Section II: Free response, 14 questions, 60 marks

Total: 70 marks.

The paper covers both Year 11 and Year 12 Extension 1 content. Multi-step extended questions in the back third of Section II combine topics: a typical Q14 might thread vectors through a projectile problem, or combine induction with combinatorics.

Bring a NESA-approved scientific calculator. Graphics calculators are not used in NSW HSC Mathematics.

How Extension 1 scales (2026)

In UAC's Report on the Scaling of the 2025 NSW HSC, Mathematics Extension 1 had a scaled mean of 39.7 per unit out of 50, the second highest among courses with 500 or more students (behind Mathematics Extension 2), and it lifts the overall ATAR aggregate significantly when sat alongside Advanced. For comparison:

• Mathematics Extension 2: 43.4 per unit (the highest in 2025)
• Mathematics Extension 1: 39.7 per unit
• Mathematics Advanced: 31.9 per unit
• Mathematics Standard 2: 23.3 per unit

UAC warns that its tables are not a conversion from HSC marks to scaled marks, and scaling is recalculated every year; see how HSC subjects are scaled. Try our HSC ATAR calculator to model your projected ATAR from Extension 1 plus your other subjects.

Bands in Extension 1 are labelled E1 to E4 rather than 1 to 6 (because it is a 1-unit course). E4 starts at 80%, E3 at 65%, E2 at 50%. Most strong cohorts aim for E3 or E4.

Study strategy

Extension 1 rewards consistent weekly practice over short, intense cramming sessions. The standard approach is:

1. Master Advanced first. Extension 1 sits on top of Advanced calculus, functions and trig. If you cannot quickly differentiate a chain-rule composite or integrate by substitution, Extension 1 questions will be unforgiving.
2. Build the syllabus into a topic-by-topic checklist. Use the dot point pages on this site as your spine.
3. Drill standard techniques. Induction, integration by substitution, vector dot product, binomial probability and the t-formula are the bread and butter of the paper.
4. Do at least 8 full past papers under timed conditions in the final two terms. Mark them honestly against the NESA marking guidelines.
5. Keep a mistakes book. Note every careless slip and re-do the question a week later.

Our 2026 deep guides

We have written in-depth guides for the high-stakes Extension 1 topics:

• HSC Maths Ext 1 binomial theorem and combinatorics deep dive
• HSC Maths Ext 1 mathematical induction deep dive
• HSC Maths Ext 1 vectors deep dive

Each guide includes worked examples, exam-style questions, and links to the relevant NESA syllabus dot points.

System context

HSC Mathematics Extension 1 sits inside the wider HSC system. Related explainers:

• How the HSC ATAR is calculated covers UAC's aggregate and scaling mechanics.
• How HSC subjects are scaled explains why Extension 1 scales much higher than Advanced or Standard.
• HSC bonus points and EAS covers subject-specific selection-rank bonuses (Mathematics Extension 1 earns bonus points at most NSW engineering, science and actuarial degrees).

How to use this hub

If you are a Year 12 student sitting HSC 2026: work through every Year 12 module dot point on this site, then return to weak Year 11 dot points. Aim for 8 to 12 timed past papers in Term 4.

If you are starting Year 12 on the new 2024 syllabus: read what's changed first, then work through the dot points for the content that carries over as your school covers it.

For the official NESA syllabus, prescribed reference material, and past papers, refer to educationstandards.nsw.edu.au.